CTC Charged Toner Conveyor
fa acceleration limited frequency
TWTT Traveling Wave Toner Transport
Ca numerical coefficient for fa 
PP Pixel Packet
Eo electric field amplitude of traveling wave
XJ XeroJet (present invention)
Vo voltage amplitude of traveling wave
DPP Digital Packet Printer (prior art)
k wave number (=xcfx80/xcex)
DP Digital Packet
xcex wavelength of traveling wave
CMYK cyan, magenta, yellow, black
f frequency of traveling wave
dpi dots per inch
q/m tribo, or charge to mass ratio of toner
v process speed of printer in cm/sec
Q/wav toner charge per unit length of wave front
ppm pages per minute
Cm numerical coefficient for Q/wav
xcfx84 period of traveling wave
M/wav toner mass per unit length of wave front
Electrostatic deposition of dry powder inks (charged toner) directly onto paper, broadly identified as direct powder printing, can be classified according to whether or not the process includes the use of control apertures to modulate the quantity of toner deposited on the paper. Examples of processes that include control apertures are Direct Electrostatic Printing (DEP), invented by Schmidlin, U.S. Pat. Nos. 4,814,796, 4,755,837 and 4,876,561, and TonerJet(trademark), invented by Larson, U.S. Pat. Nos. 5,774,159 and 5,036,341. This type of process is sensitive to wrong sign toner and requires the use of a cleaning process to clean the control apertures following every printed page. Direct powder printing processes which do not include control apertures have been disclosed by Rezanka, U.S. Pat. No. 5,148,204, Hays, U.S. Pat. No. 5,136,311, and Salmon, U.S. Pat. Nos. 5,153,617, 5,287,127 and 5,400,062.
The Salmon Patents disclose a process similar to the present invention to the extent that it utilizes a toner conveyor process. However, the toner conveyors in the Salmon Patents are very different from the Charged Toner Conveyor (CTC) (U.S. Pat. No. 4,647,179, invented by Schmidlin) in several important ways that are fully explained later on. The Salmon Patents disclose a xe2x80x9cdigital pumpingxe2x80x9d apparatus for moving discrete packets of toner, called xe2x80x9cDigital Packetsxe2x80x9d (DPs), along an array of column conveyors from a toner source at one end of the column conveyors to a receiver sheet at the other end of the column conveyors. One column conveyor is used for each pixel site to be printed across the width of a page. Each column conveyor is an independently controlled linear array of narrow electrodes, optimally five microns wide, to accommodate single rows of toner that extend the length of the electrodes. Such rows of toner are called Digital Packets (DPs). One DP consists of two to five toner particles depending on the toner size. Discrete levels of gray are printed at each pixel site on the receiver sheet by counting out the number of DPs to be deposited on that site. For example, for a 600 dpi resolution printer, 16 DPs are deposited at a single pixel site to print black, or a saturated reflection density. White or gray pixels are then formed with 0 to 15 DPs.
Transport, or xe2x80x9cdigital pumpingxe2x80x9d, of DPs in the Salmon method is achieved with three-phase digital pulses. An end view of a trapezoidal potential well is illustrated in FIG. 1. This figure depicts a moment in time when the digital voltage level of phase b is low and the voltage level of phases a and c are high. This produces a trapezoidal potential well whose spatial depth is effectively comparable to the combined width of one electrode and space. The size of the electrodes are claimed by Salmon to be optimally 5 microns so that the trapezoidal well will hold a single toner particle in the process direction (left to right in FIG. 1). The ordinate in FIG. 1 represents both voltage and distance above the conveyor surface, with their scales chosen to illustrate the effective depth of the potential well in relation to the size of the toner. The end view of a single DP is shown in FIG. 1 to illustrate this important sizing feature. xe2x80x9cDigital Pumpingxe2x80x9d moves a DP along the conveyor by cycling the low phase through the sequence b, c, a, b etc., with proper timing (c lowered slightly in advance of raising b, etc.). In this manner the trapezoidal potential well is stepped along the conveyor, carrying the DP with it. Because the potential wells are small (comparable to the size of a toner particle), the toner must move in sliding or rolling contact with the conveyor surface. Otherwise, any perturbing influence during the digital stepping process will cause a trapezoidal potential well to lose control of toner particles in a DP.
It is appropriate to recall here that movement of charged toner particles in sliding/rolling contact with a stationary solid boundary was an objective of my original CTC invention. Early experiments with CTCs, however, revealed that sliding or rolling contact of toner particles with the conveyor surface could not be achieved (cf., Fred Schmidlin, xe2x80x9cA New Nonlevitated Mode of Traveling Wave Toner Transportxe2x80x9d, IEEE Transactions on Industry Applications, Vol. 27, No. 3, May/June 1991). Instead, the toner particles were discovered to move in an aerosol state as tiny linear clouds, with one such cloud confined in the potential trough of each wave. This mode of Traveling Wave Toner Transport (TWTT), illustrated in FIG. 2, was called the xe2x80x9cSurfing Modexe2x80x9d because toner particles are pushed by a traveling electrostatic sine wave in much the same way a surf rider is pushed by a water wave. The wavelength of the traveling wave required for this mode of transport must be at least six to eight times the particle diameter. Each particle needs room on the stable part of a wave (the concave upward portion of the wave following the wave minimum) to recover its equilibrium position on a wave after being scattered by the conveyor surface or other mutually repulsive toner.
Because toner scattering is difficult to avoid on a conveyor at particle speeds of practical interest for printing applications (greater than one meter per second), it is predicted that practical implementation of the Salmon invention, called Digital Packet Printing (DPP), is not feasible or severely limited. Although DPs can be moved with toner-sized, digitally-driven xe2x80x9csquare wellsxe2x80x9d at slow speeds (as demonstrated with miniature models by Salmon), the reliability required for quality printing at practical transport speeds has not been demonstrated and is claimed to be unreliable or impractical.
Another problem with DPP, as described in the aforementioned Salmon Patents, is that the mutual repulsion of same polarity toner will also cause particles to hop uncontrollably between contiguous channel conveyors. Salmon has recently addressed this problem by incorporating barrier electrodes, or xe2x80x9cguide railsxe2x80x9d, between adjacent conveyor channels. But this feature does not prevent toner particles from skipping or slipping between DPs in the process (or propagation) direction.
Another problem with DPP is the inclusion of xe2x80x9cpacket stepxe2x80x9d and xe2x80x9cpacket holdxe2x80x9d processes wherein toner movement is stopped for periods of time. During this time, toner adhesion to the conveyor surface tends to grow with time, making it difficult to start the toner moving again. Indeed, experience has shown that toner inertia plays an important role in TWTT and collisions with other moving toner particles are generally required to get toner stalled on a conveyor moving again. Therefore, xe2x80x9cpacket holdxe2x80x9d processes are undesirable and should be avoided.
Another problem with DPP is its complexity. The proposed DPP architectures include multiple toner conveyors and xe2x80x9cwriting headsxe2x80x9d. Accurate registration and alignment of the writing heads is required for page width printing applications.
Another problem, or undesirable limitation, of DPP is its ability to print discrete density levels only. Forty-eight clock steps, or 16 xe2x80x9cwavesxe2x80x9d, are required to print one of 16 density levels (including white), at one pixel site. Therefore, the usual half-toning process commonly used in the printing industry must be used to print more than 16 levels of gray. Customary procedures, such as dot-dithering, must then be used to mask unwanted image defects, such as contouringxe2x80x94a problem that is most noticeable in the highlight areas of an image.
Another limitation of DPP is that the new method of multiplexing disclosed herein would be significantly limited if it were applied to the digital pumping process on which DPP is based.
Finally, another limitation of DPP is its process speed. As shown in my aforementioned IEEE paper, toner dynamics (inertia) limits the operating frequency and mass flow rate of traveling wave transport. The same physical constraints must limit the digital pumping process at least as severely. This is borne out in the analysis provided below.
The present invention, called xe2x80x9cXeroJetxe2x80x9d (XJ), overcomes the above problems and limitations of DPP. It is a dry powder printing process in which toner flow on a CTC is divided into parallel columns that feed an array of toner jets formed at the downstream end of the CTC. Quite apart from the details of this invention, however, its ability to overcome the limitations of DPP is predicted from well-established properties of the surfing mode of TWTT on which this invention is primarily based. This important mode of toner transport is schematically illustrated in FIG. 2. It shows the size and aerosol character of the toner in relation to the traveling sine wave that drives the surfing mode of TWTT. Note that the wavelength of the traveling sine wave is much larger than the size of the toner particles (at least six times the toner diameter) and the number of toner particles transported per unit length of wave front is much greater than the number transported via DPP. This basic feature is vital to the high toner flow rates achieved with TWTT. Indeed, recent experiments with 500 microns wavelength CTCs have demonstrated toner flow rates in excess of 25 mg/cm-sec. This is adequate to cover a receiver sheet placed at the downstream end of a CTC with one mg/cm2 of toner (enough to produce a saturated reflection density) at the speed of 25 cm/sec, or 60 pages per minute.
To provide a broad basis for the design and projected performance of CTCs for the present invention, a summary of the relevant background analysis now follows.
Toner flow on a conventional CTC is controlled by two factors. The first is the acceleration limited drive frequency, denoted by fa. As derived in the above IEEE paper, fa=Ca sqrt(Eokq/m) where q/m is the average charge to mass ratio of the toner (also known as xe2x80x9ctriboxe2x80x9d in the xerographic industry), Eo is the electric field amplitude of the wave, k is the wave number (2xcfx80/xcex), xcex is the wave length of the traveling wave and Ca is a numerical coefficient. Ca is approximately equal to 27 when Eo, k and q/m are expressed in standard mks units. Eo=kVo, where Vo is the voltage amplitude of the wave. At wave frequencies greater than fa toner particles starting from rest cannot catch a wave. The inertial force that limits fa also restores scattered particles to their equilibrium position on a wave. Therefore, the possibility of transporting toner at higher frequencies by starting the particles with an initial velocity is unlikely. The second factor controlling toner flow on a CTC is the maximum charge per unit length of wave front (Q/wav) transportable by one wave. Based on space charge limitations, this is estimated to be Q/wav=Cm 885Eo/k. Here the numerical coefficient Cm depends on how closely the toner particles come into proximity with the conveyor surface, or the degree by which the space charge of the toner neutralizes the electric field of the traveling wave. Cm is estimated to be between xc2xd and 2, when Eo and k are in volts/micron and cmxe2x88x921 respectively, giving Q/wav in pico-Coulombs per cm (pC/cm). The maximum mass per unit length of wave front that can be transported by one wave is then given by M/wav=Q/wav/(q/m). The practical unit of M/wav is xcexcg/cm when Q/wav and q/m are expressed in the practical units of pC/cm and xcexcC/gm respectively. The maximum toner mass flow on a conveyor per unit distance along a wave front is then given by dm/dt=faM/wav. The unit is mg/(cm-sec). If the toner flows onto a receiver sheet placed at the end of the conveyor, the speed of the receiver sheet will determine the collected mass per unit area. Assuming one mg/cm2 toner on a receiver sheet produces saturated reflection density, the speed of the sheet (v), in cm/sec, becomes numerically equal to the toner mass flow on the conveyor (dm/dt) in mg/(cm-sec). Toner mass flow on a conveyor (in mg/cm-sec) therefore predicts the process speed v anticipated for printer applications.
To illustrate the potential printer speeds inferred from the above analysis, graphs of the estimated process speed (v) and acceleration limited drive frequency, fa, vs. conveyor-wavelength are shown in FIGS. 3a and 3b. The curves in FIG. 3a are constructed to agree with recent experimental data at 500 microns wavelength. The experiments were performed using the values of q/m and Eo shown in the figure. The value of fa at 500 microns, using the theoretical coefficient Ca=27 (see IEEE paper), proved to match the frequency that provided the maximum toner mass flow in the experiments. Matching the magnitude of the maximum mass flow, to its analytical expression above yields Cm=0.47. To illustrate the impact of changing the control parameters (Eo, q/m and Cm), the curves in FIG. 3b are constructed with the values of theses control parameters chosen near their estimated practical upper bounds. Cm=1.3 corresponds to the maximum packing of toner in a potential well 30 microns wavelength based on their physical size, independent of their charge.
Further insight on the dependence of process speed on the physical quantities Eo, q/m and xcex can be gleaned from the overall scaling law vxcx9cEo{fraction (3/2)}(q/m)xe2x88x92xc2xdxcexxc2xd. The xcexxc2xd dependence obtained here is reflected, of course, in FIGS. 3a and 3b. It is now evident that a large field amplitude of the traveling wave (Eo) and low tribo (q/m) are also important factors contributing toward high process speed. The maximum possible value of Eo is limited by the onset of corona or electrical breakdown. With normally insulated conveyor electrodes, Eo may be as high as 9 V/xcexc for wavelengths below 500 microns. An unlimited small value of q/m, though appearing attractive here, is not possible. Further studies are needed to establish the lower limit of q/m. But the experimental data used for FIG. 3a shows that the tribo can be at least as low as 3 xcexcC/gm.
To finally predict the process speeds attainable with the printer method disclosed herein, it is sufficient to identify the potential working range of conveyor wavelengths that can be utilized. A shortest working wavelength emerges from the requirement that toner particles must have free volume to move as an aerosolxe2x80x94not in rolling/sliding contact with the conveyor surface. The volume of a traveling potential well per unit length along the wave front is proportional to xcex2, considering that both its depth and extension in the propagation direction are proportional to xcex. But due to the space charge limitation assumed earlier, the number of toner particles that can be put in this same volume grows linearly with xcex. Further considering that the toner particles are forced into contact with each other and the conveyor surface at xcex=30 microns (also forcing a sliding or rolling action), it follows that the free volume per particle available for perturbed particle movement (displacements from equilibrium) must grow in proportion to xcexxe2x88x9230. This suggests a reasonable lower bound for xcex of roughly 50 microns. This will provide adequate free space for toner particles to nudge each other or be scattered without being knocked out of the potential well transporting them.
An upper bound for xcex emerges from the image resolution desired for a specific printer application. A representative resolution requirement is 600 dpi, implying a maximum pixel size of 42 microns on a side. For TWTT, there is an inherent pixel size feature only for the process direction. This is the length of the receiver sheet covered by toner delivered by one wave, given by vxcfx84, v is the speed of the receiver sheet (or process speed) and xcfx84(=1/f) is the period of the wave. The pixel size in the cross direction is established by segmenting the linear toner clouds by means disclosed in detail later herein. For this reason, the number of 10 microns diameter toner particles contained in a 42 microns long segment of a linear toner cloud, denoted #/pix, is included in FIGS. 3a and 3b. I call this a xe2x80x9cpixel packetxe2x80x9d, and when it equals 35 (for 10 microns diameter particles) it will cover a 42 microns square pixel on the receiver sheet. For the conditions considered for FIGS. 3a, it is easily identified that the corresponding conveyor wavelength is 300 microns. For the conditions in FIG. 3b, the corresponding wavelength is 500 microns. The resolution in both cases is 600xc3x97600 dpi. Of course, any shorter wavelength would enable the same resolution but with a sacrifice of process speed. The pixel size at any other wavelength is proportional to #/pix. Considering further that possible constraints may arise from segmenting the linear toner clouds, it is estimated that the preferred wavelength range of CTCs for the present invention is 100 to 300 microns.
To facilitate comparison of the process speeds predicted above with those estimated for DPP, the graphs in FIGS. 3a and 3b are extended down to 30 microns wavelength. Although this wavelength is below the lower bound identified for TWTT, it is the wavelength considered optimal for DPP. For the conditions in FIG. 3a, the predicted speed for TWTT at xcex 30 microns would be 7 cm/sec if it were operative here. The speed estimated for DPP, on the other hand, is 4 cm/sec, assuming the accelerated limited frequency is applicable and the same toner can be used in both cases. This result is indicated by the label xe2x80x9c2xe2x80x9d in FIG. 3a. But, as shown above, the same resolution (600 dpi) with TWTT can be achieved at a wavelength of 300 microns, potentially enabling the speed to increase to 21 cm/secxe2x80x94a better than 5 to 1 speed advantage over DPP. Similarly, for the conditions in FIG. 3b, the speed for TWTT at 30 microns wavelength would be 13 cm/sec if it were again operative here. Interestingly, the #/pix proves to be just 2 particles in this case, implying a speed of 13 cm/sec for DPP as well. But in this case the wavelength for TWTT could be as high as 500 microns, implying a potential process speed of 53 cm/secxe2x80x94a 4 to 1 speed advantage over DPP. It is thus concluded that printers based on TWTT will provide a significant speed advantage over DPP.
Another well-stablished property of the surfing mode of TWTT (see my IEEE paper) that shall be exploited in the present invention is that traveling toner clouds extend less than xc2xc of a wavelength in the direction of propagation. This is key toga novel method of multiplexing that is disclosed below.
This invention relates to electrostatic printing systems and more particularly to direct powder printing processes based on the proven surfing mode of TWTT. The toner flow on a CTC is divided into an array of parallel pixel wide columns by overlaying the CTC with an array of barrier electrodes or xe2x80x9cguide railsxe2x80x9d separated by the pixel size for a desired resolution (e.g., 42 microns for 600 dpi resolution). At the downstream end of the CTC, the toner flowing down each column is formed into a toner jet that is focused onto an image receiver sheet. The barrier electrodes further divide the linear toner clouds transported by each traveling wave into pixel sized segments, called xe2x80x9cPixel Packetsxe2x80x9d (PPs). The set of PPs derived from one segmented toner cloud finally forms one complete row of pixels in a line across an image receiver. A modulating ejector electrode is also inserted in each pixel wide column of the CTC to continuously modulate the quantity of toner in a PP. This important feature enables the printing of continuous-tone images. Since the process forms dry toner jets during transfer from the conveyor to receiver, I call this new printing process xe2x80x9cXeroJetxe2x80x9d. This highlights its important dry ink feature while being similar in character to liquid ink-jets. XJ is also a continuous-flow analog process in contrast to DPP which is a digital process designed to print a limited number (16) of discrete density levels with a counted number of DPs.
The present invention also includes a novel means of multiplexing which is enabled by the fact that toner clouds on CTCs are spatially confined in the direction of transport to a small fraction (typically ⅙ to xe2x85x9) of a wavelength. This makes it possible to modulate a group of PPs in contiguous columns on, the conveyor at different times (or phases) of a wave period using a common modulating electrode. This feature is important because it results in significant structural simplicity and cost reduction with no sacrifice in process speed.
XJ provides numerous advantages over prior art in direct printing. It is capable of printing continuous-tone color images at high speeds. It should not require frequent cleaning. In contrast with DPP, it is based on a proven toner transport technology and provides a simpler, continuous flow process that utilizes a simpler, low-cost architecture. Its potential process speed is also significantly greater.
This invention provides the opportunity to make printers emulating dye-diffusion quality, at the low cost of liquid ink-jet printers, and at the speed of laser printers. Important embodiments include low-cost, continuous-tone color printers capable of printing color photographs.